This java applet demonstrates various properties of
vector fields. You can select from a number of vector fields and see how
particles move if it is treated as either a velocity
or a force field. This helps you visualize the field.

The menu in the upper right has a variety of different fields to
choose from. You can also input your own by scrolling to the bottom
of that menu and selecting "user-defined field" or "user-defined
potential".